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Arbitrage-free market models for option prices: the multi-strike case

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  • Martin Schweizer

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  • Johannes Wissel

    ()

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    Abstract

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    File URL: http://hdl.handle.net/10.1007/s00780-008-0068-6
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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 12 (2008)
    Issue (Month): 4 (October)
    Pages: 469-505

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    Handle: RePEc:spr:finsto:v:12:y:2008:i:4:p:469-505

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    Web page: http://www.springerlink.com/content/101164/

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    Related research

    Keywords: Option prices; Market model; Implied volatility; Static arbitrage; Dynamic arbitrage; Drift restrictions; Existence result; 60H10; 91B28; C60; G13;

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    References

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    1. Ledoit, Olivier & Santa-Clara, Pedro & Yan, Shu, 2002. "Relative Pricing of Options with Stochastic Volatility," University of California at Los Angeles, Anderson Graduate School of Management qt7jp8f42t, Anderson Graduate School of Management, UCLA.
    2. Wissel, Johannes, 2007. "Some results on strong solutions of SDEs with applications to interest rate models," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 720-741, June.
    3. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
    4. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor and Francis Journals, vol. 2(1), pages 45-60.
    5. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
    6. Martin Schweizer & Johannes Wissel, 2008. "Term Structures Of Implied Volatilities: Absence Of Arbitrage And Existence Results," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 77-114.
    7. Brace, Alan & Fabbri, Giorgio & Goldys, Benjamin, 2007. "An Hilbert space approach for a class of arbitrage free implied volatilities models," MPRA Paper 6321, University Library of Munich, Germany.
    8. H. Berestycki & J. Busca & I. Florent, 2002. "Asymptotics and calibration of local volatility models," Quantitative Finance, Taylor and Francis Journals, vol. 2(1), pages 61-69.
    9. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    10. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    12. Carr, Peter & Madan, Dilip B., 2005. "A note on sufficient conditions for no arbitrage," Finance Research Letters, Elsevier, vol. 2(3), pages 125-130, September.
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    Citations

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    Cited by:
    1. Pietro Siorpaes, 2013. "Price Dependence in Optimal Investment," Papers 1303.0237, arXiv.org.
    2. René Carmona & Sergey Nadtochiy, 2012. "Tangent Lévy market models," Finance and Stochastics, Springer, vol. 16(1), pages 63-104, January.
    3. Valdo Durrleman, 2010. "From implied to spot volatilities," Finance and Stochastics, Springer, vol. 14(2), pages 157-177, April.
    4. S. Kindermann & P. Mayer, 2011. "On the calibration of local jump-diffusion asset price models," Finance and Stochastics, Springer, vol. 15(4), pages 685-724, December.
    5. Jean Jacod & Philip Protter, 2010. "Risk-neutral compatibility with option prices," Finance and Stochastics, Springer, vol. 14(2), pages 285-315, April.
    6. Henrik Hult & Filip Lindskog & Johan Nykvist, 2013. "A simple time-consistent model for the forward density process," Papers 1301.4869, arXiv.org.

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